There are proposed various kinds of exhaust purifying systems in which an ignition device, which supplies fuel for combustion, is arranged upstream of an exhaust purifying catalyst located in an exhaust passage of an engine. For example, in a system disclosed in PTL 1, a first control state in which fuel is ignited by heating by a glow plug or a third state in which the heating by the glow plug is stopped is realized in an ignitable operating region. On the other hand, in an unignitable operating region, a second state in which the heating by the glow plug is performed but the fuel is not ignited or the above-mentioned third state is realized.
In a system disclosed in PTL 2, as an outside air temperature is lower, a preheat time for the catalyst is set to be the longer.